How can I randomize a value for a node?
Object Info Node's Random Output

I just discovered there is an Input node that can output a random value:
  Input -> Object Info
However, it only works for Material Shader nodes.

Here is the Blender wiki description of this node:  


  Object Info
  Information about the object instance. This can be useful
  to give some variation to a single material assigned to multiple
  instances, either manually controlled through the object index, based
  on the object location, or randomized for each instance. For example a
  Noise texture can give random colors or a Color ramp can give a range
  of colors to be randomly picked from.
  
  Note that this node only works for material shading nodes; it does
  nothing for lamp and world shading nodes.
  
  Location: Location of the object in world space.
  Object: Index Object pass index, same as in the Object Index pass.transformed.
  Material Index: Material pass index, same as in the Material Index pass.
  Random: Random number unique to a single object instance.